Name
Abstract | ||
|---|---|---|
Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in 1994: find a stable, minimum phase, rational controller that stabilizes a specified second-order plant. Although easily stated, this particular problem remained unsolved until 2002, when a solution was found using an eleventh-order controller. Our computational methods find a stabilizing third-order controller without difficulty, suggesting explicit formulas for the controller and for the closed loop system, which has only one pole with multiplicity 5. Furthermore, our analytical techniques prove that this controller is locally optimal in the sense that there is no nearby controller with the same order for which the closed loop system has all its poles further left in the complex plane. Although the focus of the paper is stabilization, once a stabilizing controller is obtained, the same computational techniques can be used to optimize various measures of the closed loop system, including its complex stability radius or Hinfin performance |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1109/TAC.2006.884944 | Automatic Control, IEEE Transactions |
Keywords | Field | DocType |
closed loop systems,concave programming,control system synthesis,polynomials,stability,Belgian chocolate stabilization,Hinfin performance,closed loop system,eleventh-order controller,fixed-order controller design,nonconvex optimization,nonsmooth optimization,nonsmooth variational analysis,polynomials,second-order plant,third-order controller,Fixed-order controller design,nonconvex optimization,nonsmooth optimization,polynomials,stability | Variational analysis,Control theory,Mathematical optimization,Optimal control,Polynomial,Control theory,Complex plane,Stability radius,Optimization problem,Minimum phase,Mathematics | Journal |
Volume | Issue | ISSN |
51 | 11 | 0018-9286 |
Citations | PageRank | References |
31 | 2.58 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James V. Burke | 1 | 753 | 113.35 |
| Didier Henrion | 2 | 987 | 88.48 |
| Adrian S. Lewis | 3 | 605 | 66.78 |
| Michael L. Overton | 4 | 634 | 590.15 |